Optimization Algorithm for Antenna Impedance Matching in Digitally Tunable Network
Kim, Sung Eun
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In this work, we explore different methods to tune the antenna impedance in mobile devices. Mismatch from antenna impedance can cause undesirable effects such as spurious emissions, channel leakages, increased noise floor, degraded receiver sensitivity and so on. With the advancement in technology, digitally tunable reactive components are now available. Thus, a feedback system with tunable circuitry and the aperture tuning method where the component is directly embedded in the antenna design are some of the popular choices of solution. The ‘look-up table’ method is currently widely adopted in wireless industry. The hardware component chain (RF chain) contains the set-up to measure Γ_in(ratio of reflected signal to transmitted signal in dB) and a circuit to be tuned according to the values found in the look-up table. The look-up table is a pre-defined calibration chart provided by the manufacturer. It is saved in the memory of the device for permanent use during its lifespan. In this thesis, in the effort to eliminate the process of creating this look-up table and also to free up large space of memory, we approach an analytical solution to predict the exact values of the component in the tunable circuit – hence, making the procedure a one-time measurement, so called the open-loop configuration. In Chapter 3, a thorough mathematical analysis has been developed to integrate the Q factors of each component into a sample pi-circuit. In such setup, the system is expected to calculate ZL (or the antenna, load) with measured Γ_in and then compute the three capacitance values that yield the best transducer gain by conjugate matching method. However, due to many non-ideal characteristics of the components, calibrating the setup and incorporating the calibration data into analytical solution becomes very challenging. Therefore, the closed-loop configuration is more useful. It collects the empirical data of Γ_in, apply the optimization algorithm and then tune the circuitry in feedback manner, until the lowest desired Γ_in is reached. (Note that there is no difference between the closed and open loop configuration in the physical set-up. ) The purpose of this thesis is to develop the optimization algorithm used in closed-loop configuration. It involves three degrees of freedom using three Digitally Tunable Capacitors (DTCs). Accordingly, the challenge of this research points to inventing a 3D-unconstrained optimization technique that is simple enough to be implemented in a microprocessor without employing complex equation-solving libraries. In Chapter 4, the Hill-Climbing algorithm is investigated to see if it provides a suitable approach for finding the global minimum Γ_in in the 3D space gradient defined by 3 variables or DTCs. The Hill Climbing method, however, will limit its solution to finding only the local minimum within the gradient. This means that the location of the solution will change with the resolution of the gradient and the search step-size. Therefore,it is expected that Hill Climbing algorithm yields different solutions depending on the increment size and the starting location of the search. Chapter 5 develops a new algorithm that is based on Grid Searching. The main idea is to grasp the picture of the entire gradient of 3D space and zoom-in closer to the global point by iteration. The challenge lies in defining the boundary of zoom-in region without leaking the global point and leaving it behind. Also, the scanning of the reduced region in each iteration must not be too rigorous – meaning requiring too many data points. All different pi-network will have its limited coverage region on Smith Chart, of which the load impedance can be matched with. Therefore, selecting the reactive component with the suitable range of capacitance is also an important step, in order to fully utilize the work of this thesis. Apart from that, the algorithm does not require any information about the antenna, frequency of operation nor the configuration of the DTCs. Overcoming these challenges will guarantee the device to have the best optimized state of impedance match, at a specific frequency. Given that the algorithm is a 3D optimization technique, the work of this research does not only apply to tuning a pi-tuner. The three DTCs can be also integrated in the aperture tuning system. Thesis Supervisor: Professor Safieddin Safavi-Naeini.